If `(A)/(2) = (B)/(3) = (C)/(4)` then `A : B : C`

Options

A. `2 : 3 : 4`
B. `4 : 3 : 2`
C. `3 : 2 : 4`
D. none of these

Answer

To solve the problem where \( \frac{A}{2} = \frac{B}{3} = \frac{C}{4} \) and we need to find the ratio \( A : B : C \), we can follow these steps:

### Step-by-Step Solution:

1. **Set the Common Value**:
Let \( k \) be the common value such that:
\[ \frac{A}{2} = k, \quad \frac{B}{3} = k, \quad \frac{C}{4} = k \]

2. **Express A, B, and C in terms of k**:
From the equations above, we can express \( A \), \( B \), and \( C \) as:
\[ A = 2k, \quad B = 3k, \quad C = 4k \]

3. **Write the Ratio A : B : C**:
Now we can write the ratio \( A : B : C \) using the expressions we found:
\[ A : B : C = 2k : 3k : 4k \]

4. **Simplify the Ratio**:
We can simplify this ratio by dividing each term by \( k \) (assuming \( k \neq 0 \)):
\[ A : B : C = 2 : 3 : 4 \]

### Final Answer:
Thus, the ratio \( A : B : C \) is \( 2 : 3 : 4 \).

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